Finite Group DatabasebetaFinite Group Databasebeta| order | 31180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1559⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C5×C1559 ⋊ C4 |
| Sylow | C1559 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic1559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C1559 | C4 |
| prime radical, cosocle | D5×C1559 | C2 |
| LCS | G ▷ C5×C1559 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7795 |
Polycyclic presentation:
2^2,5,1559|a^2=b,c^a=c^2,d^a=d^1558,c^b=c^43121 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31180, 7);